Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}7x-3y &= -5 \\ 8x-3y &= -1\end{align*}$
Answer: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-3y = -8x-1$ Divide both sides by $-3$ to isolate $y$ $y = {\dfrac{8}{3}x + \dfrac{1}{3}}$ Substitute this expression for $y$ in the first equation. $7x-3({\dfrac{8}{3}x + \dfrac{1}{3}}) = -5$ $7x - 8x - 1 = -5$ Simplify by combining terms, then solve for $x$ $-1x - 1 = -5$ $-1x = -4$ $x = 4$ Substitute $4$ for $x$ back into the top equation. $7( 4)-3y = -5$ $28-3y = -5$ $-3y = -33$ $y = 11$ The solution is $\enspace x = 4, \enspace y = 11$.